Use the table to answer the question.
Hours Miles walked
14 1
12 2
34 3
1 4
It takes Julian 12 hour to walk 2 miles. He decides to start walking in his spare time, but because he wants to make sure he has enough time to go a desired distance he created the data table. At which ratio does the constant of proportionality appear?
(1 point)
Responses

(1, 4)
left parenthesis 1 comma 4 right parenthesis

(14, 1)
left parenthesis Start Fraction 1 over 4 End Fraction comma 1 right parenthesis

(1, 14)
left parenthesis 1 comma Start Fraction 1 over 4 End Fraction right parenthesis

(4, 1)
The ratio at which the constant of proportionality appears is (1, 4).
To find the ratio at which the constant of proportionality appears in the table, we can compare the hours and miles walked for any two data points. Let's take the first two data points: (14, 1) and (12, 2).
The ratio between the hours in these two data points is 14/12.
The ratio between the miles walked in these two data points is 1/2.
We can simplify these ratios to 7/6 and 1/2, respectively.
Therefore, the ratio at which the constant of proportionality appears in the table is (7/6, 1/2).
To determine the constant of proportionality in the given data table, we need to examine the relationship between the number of hours and the miles walked. The constant of proportionality represents the ratio between these two quantities.
Looking at the data table, we can see that as the number of hours increases, the number of miles walked also increases. If we calculate the ratio of miles walked to hours for each data point, we can determine the constant of proportionality.
For example, when Julian walks for 14 hours, he covers 1 mile. So, the ratio between miles and hours is:
1 mile / 14 hours = 1/14
Similarly, for the other data points in the table, the ratios are as follows:
2 miles / 12 hours = 2/12 = 1/6
3 miles /34 hours = 3/34
4 miles / 1 hour = 4/1 = 4
Now, comparing these ratios, we can see that the constant of proportionality appears as the ratio (1, 6) in the table. Therefore, the correct answer is:
(1, 6)